Input-Output Approach to Study Energy Pathways in Transitional Boundary Layer: Focusing on Nonlinear Response to Actuation

We employed unstructured and structured input-output analyses to study the interplay between dominant flow structures governed by linear and nonlinear mechanisms in transitional shear flows. The effect of linear mechanisms is studied by employing unstructured input-output analysis. For incorporating nonlinear interactions as well, two structured input-output approaches are considered: with non-repeated blocks in the uncertainty matrix (J. Fluid Mech. vol. 927, A25) and with repeated blocks in the uncertainty matrix (Int J Robust Nonlinear Control vol. 34,7: 4881-4897). We have utilized these input-output approaches for a wide range of Reynolds numbers in the transitional plane Poiseuille flow and Blasius boundary layer. Our analysis reveals a complex interplay between dominant flow structures, which were elusive in past studies. We show that the dominant flow structures that arise from each approach comply with a hierarchical relationship that we derived in our theoretical analysis. A common feature for the considered base-flows reveals that linear mechanisms are responsible for the energy amplification, whereas the nonlinear mechanisms conserve the energy and diffuse it between oblique modes at higher Reynolds numbers at later stages of transition.